Straight Lines ...

The coordinates of two consecutive vertices $$A$$ and $$B$$ of a regular hexagon $$ABCDEF$$ are $$(1, 0)$$ and $$(2, 0)$$, respectively. The equation of the diagonal $$CE$$ is

One diagonal of a square is along the line $$8x - 15 y =0$$ and one of its vertices is $$(1, 2)$$. Then the equations of the sides of the square passing through this vertex are

The diagonals of a parallelogram $$PQRS$$ are along the lines $$x + 3y = 4$$ and $$6x - 2y = 7$$. Then $$PQRS$$ must be a

The ends of a quadrant of a circle have the coordinates (1, 3) and (3, 1). Then the centre of such a circle is

If four points are $$A(6,3),B(-3,5),C(4,-2)$$ and $$P(x,y),$$ then the ratio of the areas of $$\triangle PBC$$ and $$\triangle ABC$$ is:

$$\mathrm{P}_{1},\ \mathrm{P}_{2},\ldots\ldots.,\ \mathrm{P}_{\mathrm{n}}$$ are points on the line $$y=x$$ lying in the positive quadrant such that $$\mathrm{O}\mathrm{P}_{\mathrm{n}}=n\cdot\mathrm{O}\mathrm{P}_{\mathrm{n}-1}$$, where $$\mathrm{O}$$ is the origin. If $$\mathrm{O}\mathrm{P}_1=1$$ and the coordinates of $$\mathrm{P}_{\mathrm{n}}$$ are $$(2520\sqrt{2},2520\sqrt{2})$$, then $$n$$ is equal to

If $$A(-2,4)$$, $$B(0,0)$$ and $$C(4,2)$$ are the vertices of a $$\Delta ABC$$, then find the length of median through the vertex A.

The vertices of a triangle are $$A(3,4)$$, $$B(7,2)$$ and $$C(-2, -5)$$. Find the length of the median through the vertex A.

Determine the area of the triangle whose vertices are $$\displaystyle \left( \frac { 1 }{ 2 } ,\frac { -1 }{ 2 }  \right) ,\left( 2,\frac { -1 }{ 2 }  \right) $$ and $$\displaystyle \left( 2,\frac { \sqrt { 3 } -1 }{ 2 }  \right) $$.

Find the equation of the line that passes through the points $$(-1,0)$$ and $$(-4,12)$$